Question

There is 1000cm3 of aluminum available to cast a trophy that will be in the shape of a right square pyramid. Is this enough aluminum for a trophy that has a base edge of 10 cm and a slant height of 13 cm.

Answer 1

Yes, the volume of the trophy is 400 cm3

Answer 2

The 1000 cubic centimeters of aluminium is enough for aluminium a trophy that will be in the shape of a right square pyramid and has a base edge of 10 cm and a slant height of 13 cm.

Explanation:

The given is,

Volume of aluminium available is 1000 cubic centimeters

Shape of trophy is right square pyramid

Trophy has a base edge of 10 cm and slant height of 13 cm

Step:1

Formula for volume of right square pyramid,

`Volume, V = a^(2)(h)/(3)`.....................................(1)

Where, a - Base edge value

h - Height of pyramid

From given,

a = 10 cm

h = 13 cm

Equation (1) becomes,

`= 10^(2)((13)/(3) )`

`= (100)(4.333)`

`= 433.33 cm^(3)`

Volume of trophy = 433.33 cubic centimeters

Compare with the volume of available aluminium and volume of right square pyramid,

`Volume of available aluminium > Volume of right square pyramid`

`1000 cm^(3) > 433.33 cm^(3)`

So, the given volume of aluminium is enough to make right square pyramid shaped trophy.

Result:

The 1000 cubic centimeters of aluminium is enough for aluminium a trophy that will be in the shape of a right square pyramid and has a base edge of 10 cm and a slant height of 13 cm.